Grade 9 Mathematics Worksheet - Edupstairs

Grade 9 Mathematics Worksheet

Geometry of straight-line, circles, and triangles

Questions:

1. Read the entire question and the answers before you select the most correct answer.

Concentric circles: A Share the same radius B Share the same midpoint C Share the same midpoint but not the same radius D Share the same midpoint and the same circumference

In equilateral triangles A All the angles are equal B Two sides are equal C There are two lines of symmetry D One angle is obtuse

In scalene triangles A All the angles are equal B Two sides are equal C There are two lines of symmetry D No sides or angles are equal

In isosceles triangles A All the angles are equal B Two sides are equal C There are two lines of symmetry D One angle is obtuse

In any triangle the smallest angle is always opposite the A Smallest side B Biggest side C Middle side D Smallest or middle side

In any triangle on a flat surface or plane A The sum of two angles are not bigger than 450 B The sum of two angles are bigger than 900 C The sum of three angles are not bigger than 900 D The sum of three angles are not bigger than 1800

Edupstairs Grade R - 9 Learning



Grade 9 Mathematics Worksheet

When two lines are not parallel A The alternate angles are equal B The corresponding angles are equal C The co-interior angles are equal D The alternate angles are not equal

When two lines are parallel A The alternate angles are equal B The corresponding angles are not equal C The co-interior angles are not equal D The alternate angles are not equal

Any two straight lines on an infinite plane A Will always intersect B Will never intersect C Will always be parallel D Will never be equal

Any angle on a plane A Consists of two rays of the same length B Consists of two rays of the same length that intersect at a vertex C Consists of two rays of different lengths that intersect at a vertex D Consists of two rays of different lengths that do not intersect at a vertex

A transversal is a A Line that cuts parallel lines only B Line that cuts any number of straight lines C Line that never cuts parallel lines D Line that cuts only two parallel lines

A plane consists of A Length and breadth and height B Three dimensions C Two dimensions D Zero dimensions

An arc A Is a straight line B Has no length C Consists of two dimensions D Has length

Edupstairs Grade R - 9 Learning



Grade 9 Mathematics Worksheet

A chord of a circle A Can be the diameter B An never be the diameter C Consists of zero dimensions D Can also be called a tangent of that circle

A radius of a circle A Can be the diameter B Can never be a chord of the circle C Can be twice the diameter D Can also be called a tangent of that circle

Two interlocking circles A Can only cut in one point B Can only cut in two points C Can cut in an infinite number of points D Will never cut

Two interlocking circles with the same radius A Can only cut in one point B Can only cut in two points C Can cut in an infinite number of points D Will never cut

A tangent to a circle A Can only touch the circle in one point B Can touch the circle in two points C Can touch the circle in an infinite number of points D Will never touch the circle

2. Given: ABC and points D and E. Point D is on the extension of the straight line AC. Point E is any point. Join C and D with a straight line.

Edupstairs Grade R - 9 Learning



Grade 9 Mathematics Worksheet

B

A E

D C

i) Why can you say that angle ACB and DCB are supplementary? ii) What kind of angle pair is called supplementary? iii) Can we say that DCB is an exterior angle of a triangle? Why? iv) Give a definition of an exterior angle v) What elements (sides and vertices) does the exterior angle of a triangle have in

common with the triangle itself? vi) Describe the position of the side of the exterior angle, which does not belong to

the triangle

3. Join points A and E with a straight line. i) Does BAE have elements in common with ABC ? ii) Can BAE and BAC be called supplementary angles? Explain

4. Construct an exterior angle to ABC at vertex A, so that AB is the common side to the exterior angle and the triangle. Construct another exterior angle of ABC , at vertex A. i) What side does this second angle have in common with ABC ? ii) What does the construction of these two exterior angles consist of, if you use a ruler for it?

5. i) The intersecting lines in the figure below forms a triangle

J I

F

N

K

H

G

M

L

Edupstairs Grade R - 9 Learning



Grade 9 Mathematics Worksheet

ii) Copy this figure iii) Label all the exterior angles of the triangle and write it down iv) Define in words what kind of angle is called an exterior angle of a triangle v) How many exterior angles can be obtained at each vertex of a triangle? vi) Why can angle IF^J, NH^M and KG^L , not be called exterior angles of the

triangle? vii) What are angles IF^J, NH^M and KG^L , called relative to the interior angles of the triangle with which they share a vertex?

6. i) Mark the exterior angles of OKL . Write them down

K

I

J

P

O

Q

L N

M

ii) Why can KJI not be called an exterior angle of this triangle iii) Can KLM be called an exterior angle of this triangle? Why? iv) Write a definition of the exterior angle of a triangle

7. Draw two interlocking circles with a radius PQ of 5 cm. Your figure should look like this now. Connect the following points to get the following line segment. AB, AP, AQ, AD, CB, CP, CQ, CD.

i) Make a list of the shapes that you notice in this diagram and write the reason for classifying the shape in the table below

ii) Make a list of the other interesting relationships that you notice in the diagram and give reasons for these relationships

Edupstairs Grade R - 9 Learning



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